Edge-Simple Circuits through 10 Ordered Vertices in Square Grids

A circuit in a simple undirected graph G = (V, E) is a sequence of vertices {v1, v2, . . . , vk+1} such that v1 = vk+1 and {vi, vi+i} ∈ E for i = 1, . . . , k. A circuit C is said to be edge-simple if no edge of G is used twice in C. In this article we study the following problem: which is the largest integer k such that, given any subset of k ordered vertices of an infinite square grid, there exists an edge-simple circuit visiting the k vertices in the prescribed order? We prove that k = 10. To this end, we first provide a counterexample implying

• Type: Conference
• Year: 2009
• Where: IWOCA
• Authors: David Coudert, Frédéric Giroire, Ignasi Sau
• Keywords: Algorithms, Infinite Square Grid, IWOCA 2009, Largest Integer, Simple Undirected Graph